The point is not whether a crew can call their company, or the next FIR. The point is that AsA are not providing an ATC service. And it is happening far too often. I have seen aircraft add many, many mile to their journey to avoid TIBA areas - QF will not fly through them, where as Jetstar will. I suppose it is up to each company's risk management people to determine the response.
In the case of Ocean Sector being TIBA, I am unaware of any way that the outgoing NZ sector could provide any traffic information - there's no one on the other end of the line. They can't see into the airspace - no radar coverage. The sector to the West of Ocean would perhaps know they are coming, but would have no firm estimate apart from the AFTN generated departure message. And when the aircraft is in the TIBA, they would have to rely on the rest of the traffic doing the right thing with their broadcasts. Including foreign crew who would most likely not have a clue about operating in a TIBA and would have to brief themselves on the run, if that information was available!
If I were Joe public, I would not wish tor travel though such airspace. However, I don't think Mr and Mrs Public even know that they are in a TIBA. If they did, I think I know what the reaction would mostly be.....
Thanks,
Showa